Question: Simplify to lowest terms. $\dfrac{100}{90}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 100 and 90? $100 = 2\cdot2\cdot5\cdot5$ $90 = 2\cdot3\cdot3\cdot5$ $\mbox{GCD}(100, 90) = 2\cdot5 = 10$ $\dfrac{100}{90} = \dfrac{10 \cdot 10}{ 9\cdot 10}$ $\hphantom{\dfrac{100}{90}} = \dfrac{10}{9} \cdot \dfrac{10}{10}$ $\hphantom{\dfrac{100}{90}} = \dfrac{10}{9} \cdot 1$ $\hphantom{\dfrac{100}{90}} = \dfrac{10}{9}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{100}{90}= \dfrac{2\cdot50}{2\cdot45}= \dfrac{2\cdot 5\cdot10}{2\cdot 5\cdot9}= \dfrac{10}{9}$